SPYTrade v1.1
Akbar Rizqiansyah
06/11/2021
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## legend## == Need to Learn tidyquant? ====================================================
## Business Science offers a 1-hour course - Learning Lab #9: Performance Analysis & Portfolio Optimization with tidyquant!
## </> Learn more at: https://university.business-science.io/p/learning-labs-pro </>Find best ARIMA-GARCH model based on AIC
Note 16/11/2021 - Sometimes ugarchfit() fails to converge (example is AAPL data) for the best ARIMA lags, but converges for lower ARIMA lags. Maybe need to temporarily store the AIC of all ARIMA model, and walk backward the ARIMA model from best to worse AIC if GARCH fails to converge
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## `geom_smooth()` using formula 'y ~ x'
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## volatility
Seems like AMZN fits SGED better while MSFT fits normal better. Check if we map to the CDF, we get somewhat close to a uniform distribution
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Plot the two in a scatter plot
## `geom_smooth()` using formula 'y ~ x'
Check the correlation between the two stocks and their CDF
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## outlier
Fit a Copula to the stocks Restrict to independent, gaussian and t copula Note 16/11/2021 - Study other kinds of copula. When unrestricted, the function tries to fit a “survival BB8” copula. Not sure what that is.
## Bivariate copula: t (par = 0.65, par2 = 5.25, tau = 0.45)Fit it using copula library, should give the same result as the above
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## interval## rho.1 df
## 0.6547093 5.2453013Create n random samples from the copula, see if they look similar to the AMZN and MSFT data we had
Use the randomly generated CDF returns from the Copula and compare it with the actual return 
Use the randomly generated standardised residuals to construct a 5% VaR of a portfolio of 50% AMZN and 50% MSFT.
Steps: 1. Using the randomly generated residuals, calculate the 1 step estimate, i.e.
\[ X_{t} = ARIMA + e_t\] \[ e_t = \sigma_t * u_t\] u_t is the randomly generated standardised residuals \[ \sigma_t^2 = GARCH\]
## # A tibble: 2 x 4
## symbol exceed_num exceed_prop expected
## <chr> <int> <dbl> <dbl>
## 1 AMZN_exceed 26 0.0563 23.1
## 2 MSFT_exceed 24 0.0519 23.1Simple 2 portfolio analysis. Calculate VaR for the portfolio.
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## exceed_num exceed_prop expected_exceedance expected_shortfall weight1
## <int> <dbl> <dbl> <dbl> <dbl>
## 1 27 0.0584 23.1 -0.0415 0
## 2 27 0.0584 23.1 -0.0412 0.1
## 3 28 0.0606 23.1 -0.0400 0.2
## 4 29 0.0628 23.1 -0.0392 0.3
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## 6 26 0.0563 23.1 -0.0403 0.5
## 7 24 0.0519 23.1 -0.0381 0.6
## 8 25 0.0541 23.1 -0.0377 0.7
## 9 22 0.0476 23.1 -0.0386 0.8
## 10 21 0.0455 23.1 -0.0372 0.9
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## layoutTo do: Monte carlo VaR calculation:
VaR calculation based on this paper: https://www.sciencedirect.com/science/article/pii/S0167668709001267 Eqn. 24 to 27
\[ P(X_{p,t} \le VaR_t(\alpha))= \int_{-\infty}^{\infty} \int_{\infty}^{\frac{VaR_t(\alpha)}{2}-x_{2,t}} c(F(x_{1,t}), F(x_{2,t})|\Omega_{t-1})*f(x_{1,t}|\Omega{t-1})*f(x_{2,t}|\Omega{t-1}) dx_{1,t} dx_{2,t} = \alpha \] Where \[ X_{p,t} = wX_{1,t}+(1-w)X_{2,t}\]
Use Monte Carlo Integral to integrate over the VaR